Foundations of near sets

Peters, James F.; Wasilewski, Piotr

doi:10.1016/j.ins.2009.04.018

Cited by 101 publications

(66 citation statements)

References 40 publications

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“…This approach also has its roots in the original rough set approach to classifying objects and perception. Although near sets do not depend on set approximation [44], it is definitely the case that near sets were inspired by a fundamental idea in rough set theory enunciated by E. Orłowska in 1982 [27], namely, classes in an approximation space serve as a formal counterpart of perception. It is this insight that carries over to classes in a covering defined by a tolerance relation and provides a solid computational intelligence basis for measuring image resemblance.…”

Section: Resultsmentioning

confidence: 99%

“…Work on a basis for near sets began in 2002, mo-tivated by image analysis and inspired by a study of the perception of the nearness of perceptual objects carried out in cooperation with Z. Pawlak in [32]. This initial work led to the introduction of near sets [36], elaborated in [35,39,44]. Recently, the study of a perceptual basis for discovering resemblances between images led to a tolerance class form of near sets [39] that models human perception in a physical continuum viewed in the context of image tolerance spaces.…”

Section: Introductionmentioning

confidence: 99%

“…Kerre [57] on morphological image interpolation in magnifying colour images with sharp edges. A direct benefit of this research is an effective means of grouping together (classifying) images that correspond to each other relative to minuscule similarities in the contour, position, and spatial orientation of bounded regions in the images, especially in videos containing image sequences showing varied object movements (see, e.g., [15,16,40,42,44]). The contribution of this article is the introduction of an anisotropic waveletbased measure of image resemblance using a near set approach.…”

Section: Introductionmentioning

confidence: 99%

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Anisotropic Wavelet-Based Image Nearness Measure

Peters¹,

Puzio²

2009

IJCIS

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The problem considered in this article is how to solve the image correspondence problem in cases where it is important to measure changes in the contour, position, and spatial orientation of bounded regions. This article introduces a computational intelligence approach to the solution of this problem with anisotropic (direction dependent) wavelets and a tolerance near set approach to detecting similarities in pairs of images. Near sets are a recent generalization of rough sets introduced by Z. Pawlak during the early 1980s. Near sets resulted from a study of the perceptual basis for rough sets. Pairs of sets containing objects with similar descriptions are known as near sets. The proposed wavelet-based image nearness measure is compared with F. Hausdorff and P. Mahalanobis image distance measures. The results of three wavelet-based image resemblance measures for several well-known images, are given. A direct benefit of this research is an effective means of grouping together (classifying) images that correspond to each other relative to minuscule similarities in the contour, position, and spatial orientation of bounded regions in the images, especially in videos containing image sequences showing varied object movements. The contribution of this article is the introduction of an anisotropic wavelet-based measure of image resemblance using a near set approach.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Anisotropic Wavelet-Based Image Nearness Measure

Peters¹,

Puzio²

2009

IJCIS

Self Cite

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“…The algebraic properties of near sets are described in [19]. Recent work has considered near groups [9] and near semigroups [10].…”

Section: Introductionmentioning

confidence: 99%

Near Ideals in Near Semigroups

Bağırmaz

2018

Eur. J. Pure Appl. Math.

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“…This article introduces perceptual resemblance of plastic surgery facial images using near sets . Near sets were introduced by James Peters in 2006 [10] and formally defined in 2007 [11] and elaborated in [12]. Near sets result from a generalization of rough set theory.…”

Section: Introductionmentioning

confidence: 99%

Plastic Surgery Facial Image Correspondence: A Near Set Approach

Patnaik¹,

Sanober²

2012

IJCA

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This article introduces perceptual resemblance of plastic surgery facial images using near sets. Near sets are disjoint sets that resemble each other. Near sets facilitate measurement of similarity between objects (digital images) based on features values (obtained by probe functions) that describe the objects. Resemblance between disjoint sets occurs whenever there are observable similarities between the objects in the sets. Each list of feature values defines an object's description. Objects that are perceived as similar based on their descriptions are grouped together. These groups of similar objects can provide information and reveal patterns about objects of interest in the disjoint sets. The practical application of near set theory on the pre and post plastic surgery facial images to extract resemblance between them was introduced in this article. Facial plastic surgery can be reconstructive to correct facial feature anomalies or cosmetic to improve the appearance. Both corrective as well as cosmetic surgeries alter the original facial information to a great extent thereby posing a great challenge for face recognition algorithms. The main aim of this article is to measure the degree of resemblance of facial images before and after plastic surgery. Blepharoplasty (Eyelid surgery) and Rhinoplasty (Nose surgery) is being considered for this research work due to the maximum number of individuals and easy to differentiate faces before and after plastic surgery .tHD ,tNM and tHM is being used to measure the degree of resemblances between plastic surgery images. tHD measure shows around 100% nearness as compared to tNM and tHM for all features . These measures can also be used in increasing the efficiency of any face recognition system containing plastic surgery images.

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Foundations of near sets

Cited by 101 publications

References 40 publications

Anisotropic Wavelet-Based Image Nearness Measure

Anisotropic Wavelet-Based Image Nearness Measure

Near Ideals in Near Semigroups

Plastic Surgery Facial Image Correspondence: A Near Set Approach

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